scholarly journals Implementation of Linear Stability Theory on Hollow Cone-shaped Liquid Sheet

2020 ◽  
Vol 64 (3) ◽  
pp. 179-188
Author(s):  
Hadiseh Karimaei ◽  
Ramin Ghorbani ◽  
Seyed Mostafa Hosseinalipour
Keyword(s):  
Linear Stability ◽  
Stability Theory ◽  
Three Dimensional ◽  
Liquid Sheet ◽  
Linear Stability Theory ◽  
Gas Flows ◽  
Rocket Engines ◽  
Hollow Cone ◽  
Liquid Sheets ◽  
Centrifugal Injector

Surface instability of a swirling liquid sheet emanating from a centrifugal injector in presence of external and internal gas flows is studied in this paper. A three-dimensional flow for the liquid sheet and two-dimensional flows for external and internal gas flows are considered. The set of equations involved in this analysis differs from the earlier analyzes. In previous studies, a cylindrical liquid sheet has been considered to implement the linear theory but in this study, the linear stability theory is implemented on a cone-shaped liquid sheet for different cone angles. Actually more over than axial and tangential movements, the radial movements of liquid sheet and gas flows are considered in the present model. Due to complexity of the derived governing equations, semi-analytical and numerical methods were applied to solve them. The case study is oxidizer injector of rocket engines. Implementation of linear stability theory on a hollow cone-shaped liquid sheet better can predict instability phenomenon than the general linear stability analysis for this type of liquid sheets. The results show very close agreement with available experimental data.

scholarly journals Decomposition of the temporal growth rate in linear instability of compressible gas flows

2015 ◽  
Vol 778 ◽  
pp. 120-132 ◽  
Author(s):  
Mario Weder ◽  
Michael Gloor ◽  
Leonhard Kleiser
Keyword(s):  
Growth Rate ◽  
Energy Balance ◽  
Linear Stability ◽  
Couette Flow ◽  
Stability Theory ◽  
Compressible Flows ◽  
Linear Instability ◽  
Linear Stability Theory ◽  
Gas Flows ◽  
Temporal Growth Rate

We present a decomposition of the temporal growth rate ${\it\omega}_{i}$ which characterises the evolution of wave-like disturbances in linear stability theory for compressible flows. The decomposition is based on the disturbance energy balance by Chu (Acta Mech., vol. 1 (3), 1965, pp. 215–234) and provides terms for production, dissipation and flux of energy as components of ${\it\omega}_{i}$. The inclusion of flux terms makes our formulation applicable to unconfined flows and flows with permeable or vibrating boundaries. The decomposition sheds light on the fundamental mechanisms determining temporal growth or decay of disturbances. The additional insights gained by the proposed approach are demonstrated by an investigation of two model flows, namely compressible Couette flow and a plane compressible jet.

scholarly journals Convolutional neural network for transition modeling based on linear stability theory

2020 ◽  
Vol 5 (11) ◽  
Author(s):  
Muhammad I. Zafar ◽  
Heng Xiao ◽  
Meelan M. Choudhari ◽  
Fei Li ◽  
Chau-Lyan Chang ◽  
...  
Keyword(s):  
Neural Network ◽  
Convolutional Neural Network ◽  
Linear Stability ◽  
Stability Theory ◽  
Linear Stability Theory ◽  
Transition Modeling

scholarly journals A Comprehensive Model to Predict Simplex Atomizer Performance

1998 ◽  
Author(s):  
Y. Liao ◽  
A. T. Sakman ◽  
S. M. Jeng ◽  
M. A. Jog ◽  
M. Benjamin
Keyword(s):  
Stability Analysis ◽  
Film Thickness ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Liquid Fuel ◽  
Density Ratio ◽  
Liquid Sheet ◽  
Unstable Wave ◽  
Liquid Sheets ◽  
Breakup Model

The performance of liquid fuel atomizer has direct effects on combustion efficiency, pollutant emission and stability. Pressure swirl atomizer, or simplex atomizer, is widely used in liquid fuel combustion devices in aircraft and power generation industry. A computational, experimental, and theoretical study is conducted to predict its performance. The Arbitrary-Lagrangian-Eulerian method with finite volume scheme is employed in the CFD model. Internal flow characteristics of the simplex atomizer as well as its performance parameters such as discharge coefficient, spray angle and film thickness are predicted. A temporal linear stability analysis is performed for cylindrical liquid sheets under 3-D disturbance. The model incorporates swirling velocity component, finite film thickness and radius which are essential features of conical liquid sheets emanating from simplex atomizers. It is observed that the relative velocity between liquid and gas phase, density ratio and surface curvature enhance the interfacial aerodynamic instability. As Weber number and density ratio increase, both the wave growth rate and the unstable wave number range increase. Combination of axial and swirling velocity components is more effective than single axial component for disintegration of liquid sheet. A breakup model for conical liquid sheet is proposed. Combining the breakup model with linear stability analysis, mean drop sizes are predicted. The theoretical results are compared with measurement data and agreement is very good.

On the linear stability theory of Bénard–Marangoni convection

1989 ◽  
Vol 1 (7) ◽  
pp. 1123-1127 ◽  
Author(s):  
Rafael D. Benguria ◽  
M. Cristina Depassier
Keyword(s):  
Linear Stability ◽  
Stability Theory ◽  
Marangoni Convection ◽  
Linear Stability Theory
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